A helium balloon has a volume of 2.00 L at 101 kPa. As the balloon rises the pressure drops to 97.0 kPa. What is the new volume?

A balloon has a volume of 25.0 L at a pressure of 98.7 kPa. What will be the new volume when the pressure is 51.2 kPa?

A weather balloon is released into the atmosphere. You know the initial volume, temperature, and air pressure. What information will you need to predict its volume when it reaches its final altitude?

Helium in a steel tank is at 250 kPa, 300 K with a volume of 0.1 m3. It is used to fill a balloon. When the pressure drops to 125 kPa, the flow of helium stops by itself. If all the helium is still at 300 K, how big a balloon is produced?

The density of water is $1.0 g/cm^3.$ How many kilograms of water does a submerged $120-cm^3$ block displace? One kilogram has a force of 9.8 N. What is the buoyant force on the block?

To lift an object weighing $21,000$ N, how much force is needed on a piston with an area of $0.060 m^2$ if the platform being lifted has an area of $3.0 m^2$ ?

To lift an object weighing 20,000 N, how much force is needed on a small piston with an area of $0.072 m^2$ if the large piston has an area of $2.8 m^2?$

Explain why a gas has pressure.

A magnet was placed near a pile that contained both iron and sulfur. The magnet was moved gradually closer to the pile. As it neared the pile, the magnet started attracting small pieces of iron from the pile. Which of these statements best describes the contents of the pile?

$$\begin{array} { l } { \text { F. It is a homogeneous mixture of iron and sulfur. } } \\ { \text { G. It is a heterogeneous mixture of iron and sulfur. } } \\ { \text { H. It is a compound that contains both iron and sulfur. } } \\ { \text { I. It is a compound that can be separated by magnetism. } } \end{array}$$

A square matrix A is said to be nilpotent if $A^{k}=0$ for some positive integer k. The smallest value of k for which this equation holds is called the index of nilpotency. In each part, confirm that the matrix is nilpotent, and find the index of nil potency. (a)

$$A=\left[\begin{array}{rrrr}{0} & {0} & {0} & {0} \\ {1} & {0} & {0} & {0} \\ {2} & {1} & {0} & {0} \\ {-3} & {2} & {2} & {0}\end{array}\right]$$

(b)

$$\left[\begin{array}{llll}{0} & {0} & {0} & {0} \\ {1} & {0} & {0} & {0} \\ {2} & {1} & {0} & {0} \\ {0} & {2} & {0} & {0}\end{array}\right]$$

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A sample of nitrogen gas expands in volume from 1.6 to 5.4 L at constant temperature. Calculate the work done in joules if the gas expands (a) against a vacuum, (b) against a constant pressure of 0.80 atm, and (c) against a constant pressure of 3.7 atm. $\left(1\;\mathrm{L\cdot atm}=101.3\;\mathrm{J}\right)$

Compare the different pressures that result as you add air to a balloon and as you add air to a steel tank.

Oxygen gas having a volume of $1130$ cm$^3$ at $42.0\degree\mathrm{C}$ and a pressure of $101$ $\mathrm{kPa}$ expands until its volume is $1530$ cm$^3$ and its pressure is $106$ $\mathrm{kPa}$. Find (a) the number of moles of oxy- gen in the system and (b its final temperature.

Describe Earth’s atmosphere at sea level. How does the pressure change as the distance from Earth increases?